{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZMZN7IZ5S2AQQQVO3AA5EFNJID","short_pith_number":"pith:ZMZN7IZ5","canonical_record":{"source":{"id":"1207.5010","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-20T18:08:48Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"917080781b058c6fc7df0dcad2a58690ab773160ef9a39bc2ecfdd22fa611b6a","abstract_canon_sha256":"e0cf4f23885e2c81d26629366a03284a21a4f6d5111e0262bffd25c8b54dd45a"},"schema_version":"1.0"},"canonical_sha256":"cb32dfa33d96810842aed801d215a940ee024b1d78dc66c7b2e2edecd75fcd0c","source":{"kind":"arxiv","id":"1207.5010","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5010","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5010v3","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5010","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZMZN7IZ5S2AQ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZMZN7IZ5S2AQQQVO","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZMZN7IZ5","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZMZN7IZ5S2AQQQVO3AA5EFNJID","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5010","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-20T18:08:48Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"917080781b058c6fc7df0dcad2a58690ab773160ef9a39bc2ecfdd22fa611b6a","abstract_canon_sha256":"e0cf4f23885e2c81d26629366a03284a21a4f6d5111e0262bffd25c8b54dd45a"},"schema_version":"1.0"},"canonical_sha256":"cb32dfa33d96810842aed801d215a940ee024b1d78dc66c7b2e2edecd75fcd0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:58.671611Z","signature_b64":"TFWC3upqyUeU8j4hjeRF+WQNOFbuBlDWugV3yFLFDHqvkDzgqJ2hG609S9phcG6i1ghwEW7xS3feRMRg/KFRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb32dfa33d96810842aed801d215a940ee024b1d78dc66c7b2e2edecd75fcd0c","last_reissued_at":"2026-05-18T03:46:58.671022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:58.671022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5010","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"llO0cZcdY8vfsmUJfSX8k3YJKhAHCX5dqMVTQcyKJmGsJLxsCxu/idxqr6cqtH4GvUJ7m/rrELiw6Mg5IQkEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:39:52.191670Z"},"content_sha256":"584685f1d23567804056986085da0ab44da791aa83bca7c4f8aa762b06872fc5","schema_version":"1.0","event_id":"sha256:584685f1d23567804056986085da0ab44da791aa83bca7c4f8aa762b06872fc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZMZN7IZ5S2AQQQVO3AA5EFNJID","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The GDOF of 3-user MIMO Gaussian interference channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Inyup Kang, Jung Hyun Bae, Jungwon Lee","submitted_at":"2012-07-20T18:08:48Z","abstract_excerpt":"The paper establishes the optimal generalized degrees of freedom (GDOF) of 3-user $M \\times N$ multiple-input multiple-output (MIMO) Gaussian interference channel (GIC) in which each transmitter has $M$ antennas and each receiver has $N$ antennas. A constraint of $2M \\leq N$ is imposed so that random coding with message-splitting achieves the optimal GDOF. Unlike symmetric case, two cross channels to unintended receivers from each transmitter can have different strengths, and hence, well known Han-Kobayashi common-private message splitting would not achieve the optimal GDOF. Instead, splitting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5010","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Y5a6V8IuJqBmumDgEpCmJsfixVpDYn9Jzdj9/0JW4+Ja8brDGiBMb277FAahXPkK2jXmAP0k0gFmFcc56TxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:39:52.192012Z"},"content_sha256":"2e0eb1f1529272b01d2baeb818bc627a26923b65b227ca08d41bd056e29665b2","schema_version":"1.0","event_id":"sha256:2e0eb1f1529272b01d2baeb818bc627a26923b65b227ca08d41bd056e29665b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/bundle.json","state_url":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T17:39:52Z","links":{"resolver":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID","bundle":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/bundle.json","state":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZMZN7IZ5S2AQQQVO3AA5EFNJID","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e0cf4f23885e2c81d26629366a03284a21a4f6d5111e0262bffd25c8b54dd45a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-20T18:08:48Z","title_canon_sha256":"917080781b058c6fc7df0dcad2a58690ab773160ef9a39bc2ecfdd22fa611b6a"},"schema_version":"1.0","source":{"id":"1207.5010","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5010","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5010v3","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5010","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZMZN7IZ5S2AQ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZMZN7IZ5S2AQQQVO","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZMZN7IZ5","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:2e0eb1f1529272b01d2baeb818bc627a26923b65b227ca08d41bd056e29665b2","target":"graph","created_at":"2026-05-18T03:46:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The paper establishes the optimal generalized degrees of freedom (GDOF) of 3-user $M \\times N$ multiple-input multiple-output (MIMO) Gaussian interference channel (GIC) in which each transmitter has $M$ antennas and each receiver has $N$ antennas. A constraint of $2M \\leq N$ is imposed so that random coding with message-splitting achieves the optimal GDOF. Unlike symmetric case, two cross channels to unintended receivers from each transmitter can have different strengths, and hence, well known Han-Kobayashi common-private message splitting would not achieve the optimal GDOF. Instead, splitting","authors_text":"Inyup Kang, Jung Hyun Bae, Jungwon Lee","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-20T18:08:48Z","title":"The GDOF of 3-user MIMO Gaussian interference channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5010","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:584685f1d23567804056986085da0ab44da791aa83bca7c4f8aa762b06872fc5","target":"record","created_at":"2026-05-18T03:46:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e0cf4f23885e2c81d26629366a03284a21a4f6d5111e0262bffd25c8b54dd45a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-20T18:08:48Z","title_canon_sha256":"917080781b058c6fc7df0dcad2a58690ab773160ef9a39bc2ecfdd22fa611b6a"},"schema_version":"1.0","source":{"id":"1207.5010","kind":"arxiv","version":3}},"canonical_sha256":"cb32dfa33d96810842aed801d215a940ee024b1d78dc66c7b2e2edecd75fcd0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb32dfa33d96810842aed801d215a940ee024b1d78dc66c7b2e2edecd75fcd0c","first_computed_at":"2026-05-18T03:46:58.671022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:58.671022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TFWC3upqyUeU8j4hjeRF+WQNOFbuBlDWugV3yFLFDHqvkDzgqJ2hG609S9phcG6i1ghwEW7xS3feRMRg/KFRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:58.671611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5010","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:584685f1d23567804056986085da0ab44da791aa83bca7c4f8aa762b06872fc5","sha256:2e0eb1f1529272b01d2baeb818bc627a26923b65b227ca08d41bd056e29665b2"],"state_sha256":"2b41e28afe8ca5cf6428261728c2ca817e5dc1b662fc0fad7c5d8cf59d3c86ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MbZv+CTJv1LG8mh5VrahGodJJkC7g/r5tJft4CvJRUyIZeIfhYUHY+4nKNgi9W2s4TZttVWQFF67c0THmGe/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T17:39:52.193845Z","bundle_sha256":"b0552013a37cd3f53b0accb347d7c9fdc421faea3311d1ad825ad6e4e7a5937a"}}